code: def _pword_is_commuting(pauli_word_1, pauli_word_2, wire_map=None):
      r"""Checks if two Pauli words commute.
  
      To determine if two Pauli words commute, we can check the value of the
      symplectic inner product of their binary vector representations.
      For two binary vectors representing Pauli words, :math:`p_1 = [x_1, z_1]`
      and :math:`p_2 = [x_2, z_2],` the symplectic inner product is defined as
      :math:`\langle p_1, p_2 \rangle_{symp} = z_1 x_2^T + z_2 x_1^T`. If the symplectic
      product is :math:`0` they commute, while if it is :math:`1`, they don't commute.
  
      Args:
          pauli_word_1 (Observable): first Pauli word in commutator
          pauli_word_2 (Observable): second Pauli word in commutator
          wire_map (dict[Union[str, int], int]): dictionary containing all wire labels used in
              the Pauli word as keys, and unique integer labels as their values
  
      Returns:
          bool: returns True if the input Pauli commute, False otherwise
  
      **Example**
  
      >>> wire_map = {'a' : 0, 'b' : 1, 'c' : 2}
      >>> pauli_word_1 = qml.PauliX('a') @ qml.PauliY('b')
      >>> pauli_word_2 = qml.PauliZ('a') @ qml.PauliZ('c')
      >>> is_commuting(pauli_word_1, pauli_word_2, wire_map=wire_map)
      False
      """
  
      if wire_map is None:
          wire_map = _wire_map_from_pauli_pair(
              pauli_word_1, pauli_word_2
          )
  
      n_qubits = len(wire_map)
  
      pauli_vec_1 = pauli_to_binary(
          pauli_word_1, n_qubits=n_qubits, wire_map=wire_map
      )
      pauli_vec_2 = pauli_to_binary(
          pauli_word_2, n_qubits=n_qubits, wire_map=wire_map
      )
  
      x1, z1 = pauli_vec_1[:n_qubits], pauli_vec_1[n_qubits:]
      x2, z2 = pauli_vec_2[:n_qubits], pauli_vec_2[n_qubits:]
  
      return (np.dot(z1, x2) + np.dot(z2, x1)) % 2 == 0
  
file_path: pennylane/pennylane/ops/functions/is_commuting.py
imports: import numpy
  import pennylane
  from pennylane.pauli.utils import is_pauli_word, pauli_to_binary, _wire_map_from_pauli_pair
label_desc: Use image node_id 1 for calling a global function with example usage: _pword_is_commuting(pauli_word_1, pauli_word_2, wire_map) and returns: unknown